Low Degree Fields Ramifying Above {2, 13, 29}

Discriminant class: −754

∞ 2 13 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 29  3 5 7 11 17 19 23 31
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 3_{i} 1_{−} 1_{−} 0 754  1^{2} 3_{i} −2 −2 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 29∗ 29∗ 2  2  2 2
C_{2} 20  2  2 2 2 2  2

Discriminant class: −377

∞ 2 13 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 29 3 5 7 11 17 19 23 31
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
2. 1_{k} 2_{i} 1_{+} 1_{+} 0 377  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 13 13 1^{2} 1_{+} 29 29  2  2 2 2 2 2
C_{2} 16  2  2

Discriminant class: 29

∞ 2 13 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 13 Over p = 29 3 5 7 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
3. 0_{+} 2_{+} 2_{+} 1_{+} -1 -17 -1 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{+} 29 29 2 3  2 2 2 3 2
S_{3} 3  2 2 2 2  3 2 3

Discriminant class: 754

∞ 2 13 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 13  Over p = 29  3 5 7 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
4. 0_{+} 3_{+} 1_{−} 1_{−} 0 -754  1^{2} 3_{+} 2 2 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 29∗ 29∗  2 2 2 2
C_{2} 4  2  2